Wave loading on marine structures is the major external force to be considered in the design of such structures. The accurate prediction of the nonlinear high-order components of the wave loading has been an unresolved challenging problem. In this paper, the nonlinear harmonic components of hydrodynamic forces on a bottom-mounted vertical cylinder are investigated experimentally. A large number of experiments were conducted in the Danish Hydraulic Institute shallow water wave basin on the cylinder, both on a flat bed and a sloping bed, as part of a European collaborative research project. High-quality data sets for focused wave groups have been collected for a wide range of wave conditions. The high-order harmonic force components are separated by applying the ‘phase-inversion’ method to the measured force time histories for a crest focused wave group and the same wave group inverted. This separation method is found to work well even for locally violent nearly-breaking waves formed from bidirectional wave pairs. It is also found that the $n$ th-harmonic force scales with the $n$ th power of the envelope of both the linear undisturbed free-surface elevation and the linear force component in both time variation and amplitude. This allows estimation of the higher-order harmonic shapes and time histories from knowledge of the linear component alone. The experiments also show that the harmonic structure of the wave loading on the cylinder is virtually unaltered by the introduction of a sloping bed, depending only on the local wave properties at the cylinder. Furthermore, our new experimental results reveal that for certain wave cases the linear loading is actually less than 40 % of the total wave loading and the high-order harmonics contribute more than 60 % of the loading. The significance of this striking new result is that it reveals the importance of high-order nonlinear wave loading on offshore structures and means that such loading should be considered in their design.

The cost of wave energy converters (WECs) can be reduced significantly by integrating WECs into other marine facilities, especially in sea areas with a mild wave climate. To reduce the cost and increase the efficiency, a hybrid WEC system, comprising a linear array (medium farm) of oscillating buoy-type WECs attached to the weather side of a fixed-type floating pontoon as the base structure is proposed. The performance of the WEC array is investigated numerically using a boundary element method (BEM) based on the linear potential flow theory. The linear power take-off (PTO) damping model is used to calculate the output power of the WEC array. The performance of the WEC array and each individual WEC device is balanced by using the mean interaction factor and the individual interaction factor. To quantify the effect of the pontoon, the hydrodynamic results of the WEC arrays with and without a pontoon are compared with each other. Detailed investigations on the influence of the structural and PTO parameters are performed in a wide wave frequency range. Results show that the energy conversion efficiency of a WEC array with a properly designed pontoon is much higher than that without a pontoon. This integration scheme can achieve the efficiency improvement and construction-cost reduction of the wave energy converters.

Bragg scattering of nonlinear surface waves over a wavy bottom is studied using two-dimensional fully nonlinear numerical wave tanks (NWTs). In particular, we consider cases of high nonlinearity which lead to complex wave generation and transformations, hence possible multiple Bragg resonances. The performance of the NWTs is well verified by benchmarking experiments. Classic Bragg resonances associated with second-order triad interactions among two surface (linear incident and reflected waves) and one bottom wave components (class I), and third-order quartet interactions among three surface (linear incident and reflected waves, and second-order reflected/transmitted waves) and one bottom wave components (class III) are observed. In addition, class I Bragg resonance occurring for the second-order (rather than linear) transmitted waves, and Bragg resonance arising from quintet interactions among three surface and two bottom wave components, are newly captured. The latter is denoted class IV Bragg resonance which magnifies bottom nonlinearity. It is also found that wave reflection and transmission at class III Bragg resonance have a quadratic rather than a linear relation with the bottom slope if the bottom size increases to a certain level. The surface wave and bottom nonlinearities are found to play opposite roles in shifting the Bragg resonance conditions. Finally, the results indicate that Bragg resonances are responsible for the phenomena of beating and parasitic beating, leading to a significantly large local free surface motion in front of the depth transition.

Ning, D.; Chen, L.; Zhao, M., and Teng, B., 2016. Experimental and numerical investigation of the hydrodynamic characteristics of submerged breakwaters in waves. The interactions between nonlinear, regular waves and submerged breakwaters with rectangular or trapezoidal cross-sections were investigated both experimentally and numerically in this article, with emphasis on the effect of the shape of the breakwater on its hydrodynamic behavior. A series of experiments was carried out and used to validate a numerical model based on a fully nonlinear, two-dimensional boundary-element method. Comparisons among the numerical results of both wave elevations and wave pressures on the structure and the measured data indicate that the present numerical model is very capable of accurately predicting the hydrodynamic characteristics of submerged breakwaters in waves. Furthermore, parametric studies were conducted to investigate the influence of the existence of the seaward and rearward slopes on the effectiven...

Extreme wave runup around a simplified representative floating production, storage and offloading vessel hull with a vertical bow is studied using computational fluid dynamics, complemented by experimental and diffraction analysis. This is a highly nonlinear system involving large vessel motions and extreme surface waves, and the behaviour is important for offshore design and operations. A separation method based on phase manipulation is carried out to facilitate the extraction of harmonics associated with the Stokes expansion of nonlinear waves. The separation method is applied to numerical and experimental data, and found to work well even for a highly nonlinear wave field scattered from a freely floating ship-shaped body. It is found that both low- and high-frequency second harmonic components can lead to wave runup at significantly higher levels than predicted by a linear analysis, while the vessel motions are very close to linear. The nonlinearity in the local wave field rather than vessel motion is key for the excitation of nonlinear extreme runup.